Modeling the transmission of Piscirickettsia salmonis in farmed salmon

Farming Atlantic salmon is an economic activity of growing relevance in the southern regions of Chile. The need to increase efficiency and reach production goals, as well as restrictions on the use of water resources, had led in recent years to certain practices that proved prone to bacterial infections among the fish. Our study focuses on the impact of rickettsial bacteria in farmed salmon, and the possibility of controlling its incidence once it is established along the salmon life cicle. We used compartmental models to separate fish in their maturation stages and health status. The mathematical analysis will involve differential equations with and without delays, and linear stability principles. Our goal was to build a simple model that explains the basic mechanisms at work and provides predictions on the outcome of different control strategies.